In 1.20.2(764 protocol) was added a configuration state. I need packets in the state, but in last(5.1.0) version seems new state is absent.

How can I get this version through maven repo?

You need the latest development build for 1.20.2 support: https://ci.dmulloy2.net/job/ProtocolLib/669/

How can I also get this version through maven repository?

I'm already updated the sources and documentation several times for every project in IDEA, cleared all caches and restarted, but there's still no new configuration state packets added in 03d7be1 :/

The version tag of the latest version is 5.1.1-SNAPSHOT, not 5.1.0. This version, however, is not provided to the nexus repository AFAIK.
So you need to install it locally:

# Clone the repository:
git clone https://github.com/dmulloy2/ProtocolLib.git

# Build the latest ProtocolLib version yourself:
./gradlew build

# Install the freshly built artifact to your local maven repository
./gradlew publishToMavenLocal

This might not be the most convenient solution, but you should be able to include ProtocolLib into your main POM now:

<dependency>
    <groupId>com.comphenix.protocol</groupId>
    <artifactId>ProtocolLib</artifactId>
    <version>5.1.1-SNAPSHOT</version>
   <scope>compile</scope>
</dependency>